Digital rock analysis systems and methods that reliably predict a porosity-permeability trend

ABSTRACT

The pore structure of rocks and other materials can be determined through microscopy and subjected to digital simulation to determine the properties of fluid flows through the material. To determine a porosity-permeability over an extended range even when working from a small model, some disclosed method embodiments obtain a three-dimensional pore/matrix model of a sample; measure a distribution of porosity-related parameter variation as a function of subvolume size; measure a connectivity-related parameter as a function of subvolume size; derive a reachable porosity range as a function of subvolume size based at least in part on the distribution of porosity-related parameter variation and the connectivity-related parameter; select a subvolume size offering a maximum reachable porosity range; find permeability values associated with the maximum reachable porosity range; and display said permeability values as a function of porosity.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Provisional U.S. Application Ser.No. 61/692,541, titled “Digital Rock Analysis Systems and Methods thatReliably Predict a Porosity-Permeability Trend” and filed Aug. 23, 2012by Giuseppe De Prisco, which is incorporated herein by reference.

BACKGROUND

Microscopy offers scientists and engineers a way to gain a betterunderstanding of the materials with which they work. Under highmagnification, it becomes evident that many materials (including rockand bone) have a porous microstructure that permits fluid flows. Suchfluid flows are often of great interest, e.g., in subterraneanhydrocarbon reservoirs. Accordingly, significant efforts have beenexpended to characterize materials in terms of their flow-relatedproperties including porosity, permeability, and the relation betweenthe two.

Scientists typically characterize materials in the laboratory byapplying selected fluids with a range of pressure differentials acrossthe sample. Such tests often require weeks and are fraught withdifficulties, including requirements for high temperatures, pressures,and fluid volumes, risks of leakage and equipment failure, and impreciseinitial conditions. (Flow-related measurements are generally dependentnot only on the applied fluids and pressures, but also on the history ofthe sample. The experiment should begin with the sample in a nativestate, but this state is difficult to achieve once the sample has beenremoved from its original environment.)

Accordingly, industry has turned to digital rock analysis tocharacterize the flow-related properties of materials in a fast, safe,and repeatable fashion. A digital representation of the material's porestructure is obtained and used to characterize the flow-relatedproperties of the material. However, the size of the digitalrepresentation often proves to be an important factor in that a modelthat is too small will fail to be representative of the physicalmaterial, and a model that is too large will consume a disproportionateamount of computational resources with little or no additional benefit.In some cases the size of the model is determined by equipmentlimitations and it is necessary to make the best of it. It would bedesirable to optimize the size of the digital rock model and maximizethe amount of information that can be derived from it.

BRIEF DESCRIPTION OF THE DRAWINGS

Accordingly, there are disclosed herein digital rock analysis systemsand methods that measure permeability over an extended porosity range.In the drawings:

FIG. 1 shows an illustrative high resolution focused ion beam andscanning electron microscope.

FIG. 2 shows an illustrative high performance computing network.

FIG. 3A shows an illustrative volumetric representation of a sample.

FIG. 3B shows an illustrative coordinate system for performing sampleanalysis.

FIG. 4 shows an illustrative division of a model region into slices.

FIG. 5A shows an illustrative distribution of subvolume porosity.

FIGS. 5B-5C show illustrative distributions of porosity-relatedparameter variation.

FIG. 6 illustrates a dependence of distribution moments on subvolumesize.

FIG. 7A shows an illustrative porosity-permeability trend derived usinga randomly-positioned sub-Darcian subvolume.

FIG. 7B shows the illustrative porosity-permeability trend derived bypositioning the subvolume with conditional probability.

FIG. 8 is a flowchart of an illustrative analysis method.

It should be understood, however, that the specific embodiments given inthe drawings and detailed description below do not limit the disclosure.On the contrary, they provide the foundation for one of ordinary skillto discern the alternative forms, equivalents, and other modificationsthat are encompassed in the scope of the appended claims.

DETAILED DESCRIPTION

For context, FIG. 1 provides an illustration of a high-resolutionfocused ion beam and scanning electron microscope 100 having anobservation chamber 102 in which a sample of material is placed. Acomputer 104 is coupled to the observation chamber instrumentation tocontrol the measurement process. Software on the computer 104 interactswith a user via a user interface having one or more input devices 106(such as a keyboard, mouse, joystick, light pen, touchpad, ortouchscreen) and one or more output devices 108 (such as a display orprinter).

For high resolution imaging, the observation chamber 102 is typicallyevacuated of air and other gases. A beam of electrons or ions can berastered across the sample's surface to obtain a high resolution image.Moreover, the ion beam energy can be increased to mill away thin layersof the sample, thereby enabling sample images to be taken at multipledepths. When stacked, these images offer a three-dimensional image ofthe sample to be acquired. As an illustrative example of thepossibilities, some systems enable such imaging of a 40×40×40 micrometercube at a 10 nanometer resolution.

The system described above is only one example of the technologiesavailable for imaging a sample. Transmission electron microscopes (TEM)and three-dimensional tomographic x-ray transmission microscopes are twoother technologies that can be employed to obtain a digital model of thesample. Regardless of how the images are acquired, the followingdisclosure applies so long as the resolution is sufficient to reveal theporosity structure of the sample.

The source of the sample, such as in the instance of a rock formationsample, is not particularly limited. For rock formation samples, forexample, the sample can be sidewall cores, whole cores, drill cuttings,outcrop quarrying samples, or other sample sources which can providesuitable samples for analysis using methods according to the presentdisclosure.

FIG. 2 is an example of a larger system 200 within which the scanningmicroscope 100 can be employed. In the larger system 200, a personalworkstation 202 is coupled to the scanning microscope 100 by a localarea network (LAN) 204. The LAN 204 further enables intercommunicationbetween the scanning microscope 100, personal workstation 202, one ormore high performance computing platforms 206, and one or more sharedstorage devices 208 (such as a RAID, NAS, SAN, or the like). The highperformance computing platform 206 generally employs multiple processors212 each coupled to a local memory 214. An internal bus 216 provideshigh bandwidth communication between the multiple processors (via thelocal memories) and a network interface 220. Parallel processingsoftware resident in the memories 214 enables the multiple processors tocooperatively break down and execute the tasks to be performed in anexpedited fashion, accessing the shared storage device 208 as needed todeliver results and/or to obtain the input data and intermediateresults.

Typically, a user would employ a personal workstation 202 (such as adesktop or laptop computer) to interact with the larger system 200.Software in the memory of the personal workstation 202 causes its one ormore processors to interact with the user via a user interface, enablingthe user to, e.g., craft and execute software for processing the imagesacquired by the scanning microscope. For tasks having smallcomputational demands, the software may be executed on the personalworkstation 202, whereas computationally demanding tasks may bepreferentially run on the high performance computing platform 206.

FIG. 3A is an illustrative image 302 that might be acquired by thescanning microscope 100. This three-dimensional image is made up ofthree-dimensional volume elements (“voxels”) each having a valueindicative of the composition of the sample at that point.

FIG. 3B provides a coordinate system for a data volume 402, with the x-,y-, and z-axes intersecting at one corner of the volume. Within the datavolume, a subvolume 404 is defined. The illustrated subvolume 404 is acube having sides of length a, but other subvolume shapes mayalternatively be used, e.g., a parallelogram having the same shape asthe overall data volume, a sphere, or a tetrahedron. It is desirable,though not necessary, for the chosen subvolume shape to be scalable viaa characteristic dimension such as diameter or an edge length. Thesubvolume 404 can be defined at any position 406 within the data volume402 using a displacement vector 408 from the origin to a fixed point onthe subvolume. Similarly, sub-subvolumes can be defined and positionedwithin each subvolume. For example, FIG. 4 shows a subvolume dividedinto slices 502 perpendicular to the flow direction (in this case, thez-axis).

One way to characterize the porosity structure of a sample is todetermine an overall parameter value, e.g., porosity. The image isprocessed to categorize each voxel as representing a pore or a portionof the matrix, thereby obtaining a pore/matrix model in which each voxelis represented by a single bit indicating whether the model at thatpoint is matrix material or pore space. The total porosity of the samplecan then be determined with a straightforward counting procedure.Following the local porosity theory set forth by Hilfer, (“Transport andrelaxation phenomena in porous media” Advances in Chemical Physics,XCII, pp 299-424, 1996, and Biswal, Manwarth and Hilfer“Three-dimensional local porosity analysis of porous media” Physica A,255, pp 221-241, 1998), when given a subvolume size, the porosity ofeach possible subvolume in the model may be determined and shown in theform of a histogram (see, e.g., FIG. 5A). Note that the distributionwill vary based on subvolume size. While helpful, the distribution ofFIG. 5A reveals only a limited amount of information about theheterogeneity of the model and does not account for directionalanisotropy of the sample.

One example of a more sophisticated measure is the standard deviation ofporosity along a specific direction. As shown in FIG. 4, a volume (orsubvolume) can be divided into slices perpendicular to the flowdirection. The structure of the pores may cause the porosity to varyfrom slice to slice, from which a standard deviation of porosity alongthe flow direction can be determined. While this measure itself providesa useful indication of the pore structure, it can be extended. If thesample volume is divided into subvolumes (see, e.g., FIG. 3B) and thestandard deviation of porosity measured (relative to the averageporosity of the whole sample and normalized by that same averagedporosity) for each subvolume, it yields a histogram such as that shownin FIG. 5B. Again, this histogram is a function of the subvolume size.As the subvolume size grows from near zero to the size of arepresentative elementary volume (“REV”), the histogram converges andbecomes nearly Gaussian in shape. (By way of comparison, when thesubvolume dimension in a perfectly periodic “ideal” sample has a sizethat is an integer multiple of the REV size, the histogram is going tohave zero mean and zero variance, in other words a Dirac delta functioncentered at zero.)

The REV size depends on the statistical measure used to define it. Theforegoing approach yields an REV suitable for Darcian analysis, andhence the REV size (e.g., diameter, length, or other dimension) isreferred to herein as the “integral scale” or “Darcian scale”. Otherlength scales may also be important to the analysis. For example, thepercolation scale, defined here as the subvolume size at which theaverage difference between total porosity and the connected porosity(porosity connected in some fashion to the inlet face) falls below athreshold, for example without limitation: 1%. This difference is alsotermed “disconnected porosity”, and depending on the specific context,may be limited to as little as 1% or as much as 10%, though the upperlimit is preferably no more than 2%. Other threshold values may also besuitable, and it is believed that other definitions of percolationlength would also be suitable. See, e.g., Hilfer, R. (2002), “Review onscale dependent characterization of the microstructure of porous media”,Transp. Porous Media, 46, 373-390, doi:10.1023/A:1015014302642. We notethat the percolation scale can be larger than, or smaller than, theintegral scale, so generally speaking the larger of the two should beused to define a truly representative elementary volume.

Another measure of porosity structure is the standard deviation ofsurface-to-volume ratio. If the surface area (or in a two-dimensionalimage, the perimeter) of the pores in each slice 502 (FIG. 4) is dividedby the volume (or in 2D, the surface area) of the corresponding pores,the resulting ratio exhibits some variation from slice to slice, whichcan be measured in terms of the standard deviation. As the standarddeviation of the surface-to-volume ratio is determined for eachsubvolume in a model, a histogram such as that in FIG. 5B results. Asbefore, the histogram should converge and approximate a Gaussiandistribution when the subvolume size reaches or exceeds the integralscale.

FIG. 6 compares the moments of both histograms (standard deviation ofporosity and standard deviation of surface-to-volume ratio (SVR)) fortwo different samples as a function of subvolume size. The first fourmoments (mean, standard deviation, skew, and kurtosis) are shown forsubvolumes sizes as measured by edge length of the subvolume (which is acube) in the range from 60 to 480 units. The first moment for bothsamples approaches zero, i.e., the center of the standard deviation ofporosity and SVR distributions approaches a zero variation with respectto the porosity and SVR of the whole sample, meaning that on average thesubvolumes have the same porosity and SVR as the whole sample when thesubvolume size reaches about 200 units. The second moment for bothsamples becomes similarly close to zero at this length scale (200),i.e., the probability of a subvolume having the same standard deviationof porosity and SVR as the whole sample is quite high. The asymmetry ofthe distribution (as indicated by the skew value) and the kurtosis alsobecome small at and above this threshold, suggesting that the REV size,to define an integral length scale according to Darcy analysis, is nolarger than 200 units. As explained in U.S. Provisional Application61/618,265 titled “An efficient method for selecting representativeelementary volume in digital representations of porous media” and filedMar. 30, 2012 by inventors Giuseppe De Prisco and Jonas Toelke (andcontinuing applications thereof), either or both of these measures canbe employed to determine whether reduced-size portions of the originaldata volume adequately represent the whole for porosity- andpermeability-related analyses.

Various methods for determining permeability from a pore/matrix modelare set forth in the literature including that of Papatzacos “CellularAutomation Model for Fluid Flow in Porous Media”, Complex Systems 3(1989) 383-405. Any of these permeability measurement methods can beemployed in the current process to determine a permeability value for agiven subvolume.

As mentioned in the background, the size of the model may be constrainedby various factors including physical sample size, the microscope'sfield of view, or simply by what has been made available by anotherparty. It may be that a model is subjected to the foregoing analysis andshown to have an integral scale and/or a percolation scale that issubstantially same as the size of the model. In such a case, the size ofthe representative elementary volume should be set based on the largerof the integral scale or the percolation scale, and there are a sharplylimited number of subvolumes in the model having this size.

FIG. 7A is a graph of permeability (on a logarithmic scale) as afunction of porosity for a sample of Fountain Blue rock. The solid curveis derived from the published literature on this rock facies and isshown here solely for comparative purposes. It is desired to apply thedisclosed methods to samples for which this curve may be unknown, sothat the curve can be determined or at least estimated. Alternatively,the disclosed methods may be employed to verify that the sample actuallyexhibits the expected relationship.

The size of the whole sample in this case is larger than the REV size.When taken as a whole, the model yields only one permeability vs.porosity data point which appears in FIG. 7A as a diamond. The diamondis on the curve, indicating that the measurement is accurate. Due to thelimited amount of information this single point provides, it is desiredto extend the range of data points insofar as it is possible with thegiven model, so as to predict the permeability values for differenthypothetical members of this rock family having larger or smallerporosities.

One solution is to employ REV-sized subvolumes and independent measuretheir porosity-permeability values. This approach is only feasible ifthe whole sample is much larger than the REV size. This is often not thecase, so the measured porosity-permeability values are likely to belimited to a very small range close the measurement for the sample as awhole.

Since the model exhibits a range of subvolume porosities (see, e.g.,FIG. 5A) that increases as the subvolume size shrinks, the user may betempted to reduce the subvolume size below the REV size, making agreater number of subvolume positions available for exploring theporo-perm trend, each subvolume potentially yielding a differentporosity-permeability measurement. The triangles in FIG. 7A show theresulting measurements from a randomly-chosen set of subvolumepositions, with the subvolume having an edge length of about half thatof the REV. Notably, these data points suggest a substantially incorrectrelationship between porosity and permeability. Hence, a random-choicestrategy appears destined to fail.

Accordingly, we propose a strategy using reduced-size subvolumes withconditionally-selected positions rather than randomly chosen positions.FIG. 7B is a graph similar to FIG. 7A, but this time withconditionally-chosen subvolume positions as provided further below. Notethat the substantial majority of measurements are now aligned with thesolid curve, indicating that it is possible to extract aporosity-permeability relationship over an extended porosity range evenwhen using a subvolume size below the REV size. The porosity ranges 702,704, and 706 are referenced further below, but we note here that 702indicates the porosity range that is reachable in this sample with asubvolume dimension about half that of the REV size, variation below athreshold of 40% of the mode of the standard deviation of porositydistribution, and disconnected porosity of no more than 1% of thesubvolume's total porosity. Porosity range 704 indicates the regionwhere the average disconnected porosity lies between 1% and 10%, andporosity range 706 indicates the region where the average disconnectedporosity is on the order of 20%.

Given the foregoing principles and practices, we turn now to adiscussion of certain methods that enable determination of aporosity-permeability relationship over an extended porosity range whenanalyzing a small digital rock model. FIG. 8 is an illustrativeflowchart to support this discussion.

The illustrative workflow begins in block 802, where the system obtainsone or more images of the sample, e.g., with a scanning microscope ortomographic x-ray transmission microscope. Of course the images can bealternatively supplied as data files on an information storage medium.In block 804, the system processes the images to derive a pore/matrixmodel. Such processing can involve sophisticated filtering as set forthin existing literature to classify each image voxel as representing apore or a portion of the matrix.

In block 806, the system determines a flow axis. This determination maybe based on external factors (e.g., the orientation of the materialsample relative to the well, formation pressure gradients, clientspecifications). When the axis is not based on external factors, it maybe selected based on an analysis of the pore/matrix model (e.g.,choosing the axis with the highest absolute permeability, or the axishaving the lowest standard deviation of porosity).

In block 808, the system finds the distributions of standard deviationof porosity (e.g., FIG. 5B) at different subvolume sizes, distributionsof standard deviation of surface to volume ratio (e.g., FIG. 5C), and/orother distributions of porosity-related parameter variation as afunction of subvolume size. From these distributions, the systemdetermines a (Darcian) integral scale. Note that for a usefulporosity-permeability trend to be extractable, we believe that thedimensions of the original model should be at least four or five timesthe dimensions of the REV.

In block 810, the system finds a measure of pore connectivity atdifferent subvolume sizes. The connectivity can be characterized in avariety of ways, including finding a percentage or normalized volume ofthe subvolume pore space connected to an inlet face of the pore/matrixmodel. In accordance with the Hilfer's Local Porosity theory, ahistogram of the subvolume connectivities will exhibit a mean and amode, either of which could be used as a connectivity measure. As analternative, the percentage difference between the total subvolume porespace and the subvolume pore space connected to an inlet face (hereaftertermed the disconnected pore percentage) can be used. From therelationship between the connectivity measure and subvolume size, thesystem determines a percolation scale, e.g., as one step above thelargest subvolume size with a disconnected pore percentage below athreshold.

In block 811, the system determines whether the whole model size issubstantially (four or five times) bigger than the larger of thepercolation scale or the integral scale. If the model is substantiallybigger than the larger of these scales, an adequate porosity rangeshould be reachable using a subvolume size equal to the larger of thesetwo scales. Hence the system proceeds with a systematic (potentially apseudo-random), unconditional selection of subvolumes and in block 816determines the porosity-permeability value associated with eachsubvolume. A plot of these data points, with an optional matching curvedetermined in block 817, should reveal the porosity-permeabilityrelationship for the sample.

Otherwise, when the whole model size is approximately the same as thelarger of the percolation or integral scales, it is desirable to derivethis relationship using smaller (sub-REV) subvolumes. (This might not bepossible if the larger of the two scales is the percolation scale.) Inblock 812, the system determines a reachable porosity, either for agiven subvolume size or for each of multiple subvolume sizes. Aspreviously mentioned, for a given size, each subvolume position yields adifferent potential measurement on the porosity-permeability space.However, when operating in the sub-REV domain, not all subvolumes areused to extract the poro-perm trend. Rather, the system performs aconditional probability analysis, placing one or more conditions onwhich subvolumes can be employed in this analysis. One condition is thatthe standard deviation of porosity of the subvolume should not vary toomuch from the standard deviation of porosity of the full model.Accordingly, the system requires that the subvolume have a standarddeviation of porosity below a given threshold (hereafter termed the“variation threshold”). In one embodiment, this threshold is set at the20^(th) percentile, meaning that the subvolume should have a standarddeviation in the bottom fifth of the distribution (in FIG. 5B, thiswould be below about 0.16). In another embodiment, the variationthreshold is set at the 40^(th) percentile (about 0.19 in FIG. 5B). Somesystem embodiments may employ a similar threshold on the standarddeviation of SVR as an additional or alternative condition.

Another condition that may be imposed by the system is that thesubvolume have only a disconnected porosity that is below a giventhreshold (hereafter termed the “connectivity threshold”). In oneembodiment, the system requires that the subvolume have no more than 1%disconnected porosity. In another embodiment, the system allows up to 2%disconnected porosity. In a preferred system embodiment, the subvolumemust be below both the variation threshold and the connectivitythreshold. The range of porosities possessed by subvolumes satisfyingthese conditions is the “reachable porosity”. In FIG. 7B, range 702 isthe reachable porosity for subvolumes having an edge size of about 50%that of the REV below the 40^(th) percentile threshold with no more than1% disconnected porosity. The system optionally adjusts the thresholdsto determine the effect on the reachable porosity range and the datapoint scatter. For example, it may be the case that only a smallsacrifice in range is made by reducing the connectivity threshold from10% to 4%, but a significant reduction in scatter may be achievable bythis reduction. Conversely, the system may determine that a variationthreshold of the 20^(th) percentile yields an insufficient range ofreachable porosity and accordingly increases the variation threshold tothe 40^(th) percentile to achieve the desired range. The system may varythe thresholds to extract this information, and in block 814 select thethreshold values that yield the best results (i.e., maximum reachableporosity that still yields with acceptable data scatter).

In block 816, the system determines the porosity-permeabilitymeasurements for the selected subvolumes satisfying the screeningconditions. In block 817, the system optionally fits a curve to the datapoints and/or provides a comparison curve derived from the literature.The resulting relationship can then be displayed to a user, e.g., in aform similar to FIG. 7B.

For explanatory purposes, the operations of the foregoing method havebeen described as occurring in an ordered, sequential manner, but itshould be understood that at least some of the operations can occur in adifferent order, in parallel, and/or in an asynchronous manner.

Numerous variations and modifications will become apparent to thoseskilled in the art once the above disclosure is fully appreciated. Forexample, the foregoing disclosure describes illustrative statistics fordetermining an REV size, but other suitable statistics exist and can beemployed. It is intended that the following claims be interpreted toembrace all such variations and modifications.

What is claimed is:
 1. A permeability determination method thatcomprises: obtaining a three-dimensional pore/matrix model of a sample;measuring a distribution of porosity-related parameter variation as afunction of subvolume size; measuring a connectivity-related parameteras a function of subvolume size; deriving a reachable porosity range asa function of subvolume size based at least in part on the distributionof porosity-related parameter variation and the connectivity-relatedparameter; selecting a subvolume size offering a maximum reachableporosity range; finding permeability values associated with the maximumreachable porosity range; and displaying said permeability values as afunction of porosity.
 2. The method of claim 1, further comprisingdetermining an integral scale based at least in part on saiddistribution of porosity-related parameter variation as a function ofsubvolume size.
 3. The method of claim 2, further comprising determininga percolation scale based at least in part on the connectivity-relatedparameter as a function of subvolume size.
 4. The method of claim 1,wherein said deriving and selecting are conditioned upon determiningthat at least one of an integral scale and a percolation scale arecomparable to a dimension of the pore/matrix model.
 5. The method ofclaim 1, wherein said obtaining includes: scanning a physical rocksample to obtain a three-dimensional digital image; and deriving thepore/matrix model from the three-dimensional image.
 6. The method ofclaim 1, wherein the distribution of porosity-related parametervariation is a distribution of standard deviation of porosity.
 7. Themethod of claim 6, further comprising measuring a distribution ofstandard deviation of pore surface to volume ratio.
 8. The method ofclaim 1, wherein said deriving a reachable porosity range includes:screening out subvolumes having porosity-related parameter variationabove a given variation threshold; screening out subvolumes having aconnectivity-related parameter value above a given connectivitythreshold; and determining a range of porosities associated with anyremaining subvolumes.
 9. The method of claim 8, wherein the variationthreshold screens subvolumes having variation in an upper ⅗ of thedistribution.
 10. The method of claim 8, wherein the connectivitythreshold screens subvolumes having more than 10% disconnected porosity.11. A permeability determination system that comprises: a memory havingsoftware; and one or more processors coupled to the memory to executethe software, the software causing the one or more processors to: obtaina three-dimensional pore/matrix model of a sample; measure adistribution of porosity-related parameter variation as a function ofsubvolume size; measure a connectivity-related parameter as a functionof subvolume size; derive a reachable porosity range as a function ofsubvolume size based at least in part on the distribution ofporosity-related parameter variation and the connectivity-relatedparameter; select a subvolume size offering a maximum reachable porosityrange; find permeability values associated with the maximum reachableporosity range; and display said permeability values as a function ofporosity.
 12. The system of claim 11, wherein the software furthercauses the one or more processors to determine an integral scale basedat least in part on said distribution of porosity-related parametervariation as a function of subvolume size.
 13. The system of claim 12,wherein the software further causes the one or more processors todetermine a percolation scale based at least in part on theconnectivity-related parameter as a function of subvolume size.
 14. Thesystem of claim 11, wherein said deriving and selecting are conditionedupon determining that at least one of an integral scale and apercolation scale are comparable to a dimension of the pore/matrixmodel.
 15. The system of claim 11, wherein as part of said obtaining,the software causes the one or more processors to: retrieve athree-dimensional digital image of a scanned physical rock sample; andderive the pore/matrix model from the three-dimensional image.
 16. Thesystem of claim 11, wherein the distribution of porosity-relatedparameter variation is a distribution of standard deviation of porosity.17. The system of claim 16, wherein the software further causes the oneor more processors to measure a distribution of standard deviation ofpore surface to volume ratio.
 18. The system of claim 11, wherein aspart of said deriving a reachable porosity range, the software causesthe one or more processors to: screen out subvolumes havingporosity-related parameter variation above a given variation threshold;screen out subvolumes having a connectivity-related parameter valueabove a given connectivity threshold; and determine a range ofporosities associated with any remaining subvolumes.
 19. The system ofclaim 18, wherein the variation threshold screens subvolumes havingvariation in an upper ⅗ of the distribution.
 20. The system of claim 18,wherein the connectivity threshold screens subvolumes having more than10% disconnected porosity.